A justice of the peace throughout the state may issue his warrant for any offense committed in any county, which may be directed to the sheriff of any county or his deputy or to any constable or police officer of any town in the state.
N.H. Rev. Stat. Ann. § 592-A:5
Justice of the Peace Throughout the State
Source
Official source: New Hampshire General Court. Reproduced from public-domain New Hampshire statutes; confirm against the official source for the current text. Not legal advice.